Ignorance is a very important factor in the dramatic development of Oedipus Rex, for it is Oedipus's ignorance of his true parentage that drives most of his actions, whether it's solving the Riddle of the Sphinx or inadvertently bumping off his old man.
Ignorance gives him wings, as it were, making him determined to get to the bottom of old King Laius's murder. Had Oedipus known all along that he was Laius's son, and that he was the one who murdered him, then the play would've been considerably shorter than it is. But even when the blind prophet, Tiresias, reveals the whole sordid truth to Oedipus, the proud king of Thebes doesn't want to hear about it; he prefers to remain ignorant.
This is willful ignorance, different from the kind that comes from simply not knowing. Jocasta has much the same attitude as her son/husband; she joins with Oedipus in casting doubt on the veracity of Tiresias's prophecy. In both cases, however, the truth in all its terrible majesty cannot be avoided, and the consequences of such willful ignorance are tragic indeed for the royal house of Thebes.